# On the Statistical Physics of Wealth Distribution

## TL;DR

This paper develops a spectral analysis framework to compare asset exchange models with real-world Ethereum transaction data, enhancing understanding of wealth distribution dynamics and validating theoretical models.

## Contribution

It introduces a spectral approach to validate asset exchange models against blockchain data, linking spectral properties to wealth distribution and external factors.

## Key findings

- Spectral properties differ between equilibrium and non-equilibrium systems.
- Ethereum price changes correlate with spectral shifts in transition matrices.
- External factors like taxes influence wealth evolution and initial distribution dependence.

## Abstract

Asset exchange models (AEMs) provide a physics-inspired framework for studying wealth formation. These models capture wealth distribution dynamics via pairwise money exchanges, yielding steady-state distributions from exponential to heavy-tailed power laws. However, empirical validation remains limited due to scarce real-world transaction data. Here, we bridge this gap by analyzing spectral properties of Markov transition matrices from both AEMs and Ethereum blockchain data, enabling quantitative comparison of model and empirical exchange dynamics. We assess thermodynamic equilibrium in exchange processes - specifically, detailed balance - and derive steady-state wealth distributions from transition matrices. We find that equilibrium systems' spectra contain only real eigenvalues and link Ethereum price changes to spectral shifts. We also investigate external factors (e.g., taxes), showing that advantages for richer individuals make wealth evolution path-dependent on initial distributions. Our work establishes a quantitative framework for validating AEMs with real data, advancing economic modeling and understanding of wealth formation.